This report contains different plots and tables that may be relevant for analysing the results. Observe:
alg1Given a problem consisting of \(m\)
subproblems with \(Y_N^s\) given for
each subproblem \(s\), we use a
filtering algorithm to find \(Y_N\)
(alg1).
The following instance/problem groups are generated given:
u and l. [4 options]Note that the width of objective \(i = 1, \ldots p\), \(w_i = [l_i, u_i]\) should be approx. \(10000m\). Check:
## # A tibble: 4 × 6
## m mean_width1 mean_width2 mean_width3 mean_width4 mean_width5
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 19317. 19288. 19326. 19135. 18887.
## 2 3 28356. 28479. 28149. 28047. 27084.
## 3 4 38363. 38506. 38373. NaN NaN
## 4 5 47502. 47820. 47251. NaN NaN
What is \(|Y_N|\) given the different methods of generating the set of nondominated points for the subproblems?
## # A tibble: 4 × 3
## method mean_card n
## <chr> <dbl> <int>
## 1 l 61102. 170
## 2 m 59347. 170
## 3 u 59424. 170
## 4 ul 56146. 170
Does \(p\) have an effect?
## # A tibble: 16 × 4
## # Groups: method [4]
## method p mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 3248. 50
## 2 m 2 2295. 50
## 3 u 2 741. 50
## 4 ul 2 946. 50
## 5 l 3 18814. 50
## 6 m 3 14861. 50
## 7 u 3 4405. 50
## 8 ul 3 6358. 50
## 9 l 4 91921. 35
## 10 m 4 107441. 35
## 11 u 4 95680. 35
## 12 ul 4 90554. 35
## 13 l 5 173344. 35
## 14 m 5 156307. 35
## 15 u 5 185597. 35
## 16 ul 5 171720. 35
Does \(m\) have an effect?
## # A tibble: 16 × 4
## # Groups: method [4]
## method m mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 37198. 100
## 2 m 2 43615. 100
## 3 u 2 36622. 100
## 4 ul 2 35269. 100
## 5 l 3 148973. 40
## 6 m 3 131004. 40
## 7 u 3 157511. 40
## 8 ul 3 145011. 40
## 9 l 4 21163 20
## 10 m 4 15508. 20
## 11 u 4 4136. 20
## 12 ul 4 6950. 20
## 13 l 5 28539. 10
## 14 m 5 17719. 10
## 15 u 5 5657. 10
## 16 ul 5 7844. 10
We classify the nondominated points into, extreme, supported non-extreme and unsupported.